Question

Below you are given a partial computer output from a multiple regression analysis based on a sample of 16 observations.

Answer 1

Answer:

4. ± 3.012

Step-by-step explanation:

Hello!

Assuming that for both variables X₁ and X₂ n₁= n₂ = 16

You need to test at 1% if the variable is significant, this means, if the slope for X₁ is different from zero (β₁≠0) using the t-statistic and the critical value approach.

The hypotheses are:

H₀: β₁= 0

H₁: β₁≠ 0

α: 0.01

$t= \frac{b_1-\beta_1}{Sb_1} ~t_{n_1-3}$

The degrees of freedom "n₁-3" are determined by the number of parameters that you estimate for the multiple regression, in this case there are three "β₁" "β₂" and "δ²e"

The rejection region for this test is two-tailed, the critical values are:

±$t_{n-3;1-\alpha /2}= t_{13;0.995}= 3.012$

I hope this helps!